Is y=x+8 greater rate of change than (4,10), (2,6)? Yes or no

Answer 1

To determine which has a greater rate of change, we need to compare the slope of the line represented by the equation \( y = x + 8 \) with the slope of the line passing through the points \((4, 10)\) and \((2, 6)\).

First, let's find the slope of the line \( y = x + 8 \):

The equation is in the form \( y = mx + b \), where \( m \) is the slope. Here, the slope \( m \) is 1.

Next, let's find the slope of the line passing through the points \((4, 10)\) and \((2, 6)\):

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting the given points:

\[ m = \frac{6 - 10}{2 - 4} = \frac{-4}{-2} = 2 \]

So, the slope of the line passing through \((4, 10)\) and \((2, 6)\) is 2.

Now we can compare the slopes:
- The slope of the line \( y = x + 8 \) is 1.
- The slope of the line passing through \((4, 10)\) and \((2, 6)\) is 2.

Since 2 is greater than 1, the line passing through \((4, 10)\) and \((2, 6)\) has a greater rate of change than the line \( y = x + 8 \).

The answer is no.